If we have a group of objects initially at rest in outer space, gravitational attraction will cause all the objects to crunch together into a smaller volume.
Does this mean that gravity is causing entropy to decrease, thereby violating the Second Law of Thermodynamics?
To simplify the analysis, let us first consider a scenario where we have two objects initially at rest, with perfectly elastic collisions.
The conservation of energy dictates that this pattern will keep repeating forever, with the gravitational potential energy being transformed into kinetic energy, and then back into gravitational potential energy.
If we instead consider the more realistic scenario where the collisions are not perfectly elastic, the system will lose energy with time.
The energy lost from the system is converted into photons, most of which will be infrared light, invisible to the human eye.
In our original scenario, the gravitational potential energy was transformed into the kinetic energy of the thermal vibrations.
As our system cooled down, the kinetic energy of the thermal vibrations was transformed into the energy of photons, represented here as fuzzy yellow spheres.
These photons disperse energy throughout the Universe.
This means that the entropy of the Universe is increasing, and the Second Law of Thermodynamics is not violated.
Let’s now consider the hypothetical case of a closed Universe with no dark energy, where gravity causes the entire Universe to eventually contract.
Even as the size of the entire Universe is contracting, the entropy of the Universe is still increasing, because the stars and other objects continue to emit photons, thereby causing energy to be more and more dispersed.
Entropy is a measure of how many different ways something can occur.
Here, the objects can be anywhere in the original 10 by 10 grid with equal probability.
Each individual combination of positions is therefore equally likely, regardless of whether the objects end up being located in the small 2 by 2 grid, or the slightly larger 4 by 4 grid.
There are many more combinations of positions in which the objects end up being located in the larger 4 by 4 grid, and this is what we refer to as a higher entropy.
However, entropy is not just a measure of how many different ways the positions of the objects can be distributed.
Entropy is also a measure of how many different ways the velocities and energies can be distributed.
We have to take into account all the different possible directions and magnitudes for the velocities.
During the initial conditions of our original example, the velocity of all the objects was zero, which means that there was only one way the velocities could have been distributed.
As gravity causes the velocities of the objects to increase, there are now many different ways the velocities can be distributed among the objects, and hence this means a higher entropy.
As the kinetic energy is converted into the energy of the photons, there are now more ways that the energy can be distributed throughout the universe, and this means a higher entropy.
Hence, the Second Law of Thermodynamics is not violated.
Much more information is available in the video "Thermodynamics and the End of the Universe" and in the other videos on this channel.
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